Final answer:
The straight-line distance between point X and point Y is approximately 1262 m, while the shortest distance along the roads is 1760 m.
Step-by-step explanation:
The student has asked how to calculate the straight-line distance between point X and point Y, and the shortest distance along the roads between these two points.
a) Straight-line distance calculation:
Point X is located at the junction of 15th Street and 9th Avenue, while point Y is at the junction of 24th Street and 5th Avenue. There are 9 streets between 15th and 24th Streets (24-15), and 4 avenues between 9th and 5th Avenues (9-5).
So, the horizontal distance is 9 streets × 80 m/street = 720 m, and the vertical distance is 4 avenues × 260 m/avenue = 1040 m.
The straight-line distance can be found using the Pythagorean theorem: √(720² + 1040²) ≈ √(518400 + 1081600) ≈ √1593600 ≈ 1262 m (to the nearest metre).
b) Shortest road distance:
To travel along the roads from point X to point Y, one would first traverse 9 streets and then 4 avenues (or vice versa) for the shortest path.
Therefore, the shortest road distance is the horizontal distance plus the vertical distance: 720 m + 1040 m = 1760 m.